Cells in Series and Battery Voltage

What you’ll learn

Add cell voltages with their orientations accounted for.

បូកតង់ស្យុងសែលជាស៊េរីដោយគិតទិសតភ្ជាប់។

Meaning and use

In an ideal series arrangement, cell electromotive forces add algebraically. Cells aiding one another increase the total; an opposing cell subtracts. The measured terminal voltage under load can differ because real cells have internal resistance.

សែលតស៊េរីមានតង់ស្យុងសរុបជាផលបូកមានសញ្ញា។ បើទិសផ្ទុយ ត្រូវដក។ សែលពិតអាចមានតង់ស្យុងក្រោមបន្ទុកខុសពីតម្លៃឧត្តមគតិ។

Formulas

Ideal series-cell source

\[\mathcal{E}_{\mathrm{total}}=\mathcal{E}_1+\mathcal{E}_2+\cdots\]

Opposing orientations

\[\mathcal{E}_{\mathrm{total}}=\mathcal{E}_1-\mathcal{E}_2\]

Symbols and units

Symbol	Meaning	Unit or restriction
ℰ	Electromotive force of a cell or combination	volt (V)
Series	Cells connected along one path	Connection arrangement
Orientation	Polarity relative to the chosen direction	Determines plus or minus sign

Conditions and limits

• These calculations neglect internal resistance and assume specified polarities.
• Do not use this series-addition rule for cells connected in parallel.
• គំរូនេះមិនរាប់រេស៊ីស្តង់ខាងក្នុងសែលទេ។

Worked examples

Aiding cells

Three ideal 1.5 V cells aid one another in series.

1. Add the sources: \(1.5+1.5+1.5=4.5\) V.

4.5 V

សែលទិសជួយគ្នាបូកតង់ស្យុង។

An opposing cell

A 3 V cell is opposed by a 1.5 V cell.

1. Choose the 3 V source direction as positive.
2. Net source \(3-1.5=1.5\) V.

1.5 V in the chosen positive direction

សែលទិសផ្ទុយរួមចំណែកជាសញ្ញាដក។

Common mistakes

Instead of	Use	Why
Every pair of cells adds regardless of polarity.	Account for the orientation of each cell.	Opposing sources subtract algebraically.
Two ideal 1.5 V parallel cells produce 3 V.	The series-addition rule does not apply to a parallel arrangement.	Connection type matters.

Practice

Solve these before revealing the worked solutions. Include units where relevant.

សាកល្បងដោះស្រាយមុនបើកមើលចម្លើយ។ សូមបង្ហាញជំហាន និងឯកតាដែលពាក់ព័ន្ធ។

1. Four aiding ideal 1.5 V cells are in series. Find total emf.
2. A 6 V source is opposed by a 2 V source. Find net emf.
3. Why might measured terminal voltage under load be lower than the ideal sum?

Answers and steps

Show solutions / បង្ហាញដំណោះស្រាយ

1. 6 V

   4 × 1.5 = 6.

2. 4 V toward the 6 V source’s direction

   6 − 2 = 4.

3. Real cells can have internal resistance.

   The ideal model omits that voltage drop.

Quick recap

• Check connection type and polarity.
• Add ideal series sources algebraically.
• Distinguish ideal emf from loaded terminal voltage.